Question

In: Statistics and Probability

Caption: Princess Foods wants to determine if there is a relationship in the amount a household...

Caption: Princess Foods wants to determine if there is a relationship in the amount a household spends on prepared foods to family size and income. Parthika: Well, we still have data collected from a previous marketing study. Let’s use that. We have an Excel file. I am sure we can find the spreadsheet. It should have the exact information we need. Liwei: Yes, this could be interesting. We may find enough evidence to rethink the meal preparation kits again. Bonnie: Great idea. We need to know it the data is a good fit and what the exact relationship is between the dependent variable and the independent variables. We can use this information to help us design perhaps a new line of prepared frozen foods. ParthikaYes, what about the prepackaged salad bowls. We really need to see this data. Bonnie: Yes, let’s get right on this.

Please use the below data to determine the equation that represents the relationship and explain the goodness of fit. Based on the data, write a detailed memo/explanation and interpret the results. How might this data be used?

Dollars spent on Prepared food Family size Gross monthly income
495.86 4 3126
642.77 5 3933
364.81 3 1925
619.3 5 3736
238.71 1 1453
378.94 2 2538
302.58 1 1798
231.74 2 1189
428.67 3 2247
286.99 3 1460
268.81 1 1567
329.81 2 1622
627.25 5 3828
421.52 3 2782
656.38 5 3978
400.64 3 2493
603.41 6 3753
560.69 4 3778
623 5 3609
416.12 2 2262
323.9 1 1966
418.78 3 2736
506.46 4 3274
552.53 2 3480
586.46 4 3741
637.18 8 3684
244.49 2 1476
507.19 5 2835
512.56 5 2873
312.89 1 1618
329.05 2 1565
243.49 2 1582
560.37 8 3380
599.9 5 3922
657.09 5 3845
394.82 2 2233
556.42 4 3098
596.05 8 3707
365.8 4 2071
489.08 3 3166

Solutions

Expert Solution

Excel > Data > Data Analysis > Regression > Give X and Y values range (select lables if present) > OK  

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.980501258
R Square 0.961382717
Adjusted R Square 0.959295296
Standard Error 27.83077172
Observations 40
ANOVA
df SS MS F Significance F
Regression 2 713455.378 356727.689 460.5601123 7.16905E-27
Residual 37 28658.41861 774.5518544
Total 39 742113.7966
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 61.42165489 14.32509969 4.287694761 0.00012396 32.39624586 90.44706391 32.39624586 90.44706391
Family size 9.693091949 3.607684799 2.686790141 0.01074241 2.3832282 17.0029557 2.3832282 17.0029557
Gross monthly income 0.132165589 0.007535354 17.5393996 1.6178E-19 0.116897511 0.147433667 0.116897511 0.147433667

Dollars spent on Prepared food = 61.4217 + 9.6931 * Family size + 0.1322 * Gross monthly income

If family size increases 1 unit then Dollars spent on Prepared food increases 9.6931 units when other independent variables constant

If Gross monthly income increases 1 unit then Dollars spent on Prepared food increases  0.1322 units when other independent variables constant

If Independent variables are equal to 0 then Y intercept is the mean value of Dollars spent on Prepared food

R = 0.9805, means Strong and positive correlation present

R^2 = 0.9614, means 96.14% of variation in Y variable is explained by regression model

R^2 represents goodness of fit also. If it is nearer to 1, which means it is best fit

orchestra answered 2 years ago
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